NARRATION:Back in the deepest, darkest depths of time, there lived a great mathemagician called Hypatia. Numbers fell under her spell one by one. With them, Hypatia could do anything. Now Hypatia is looking for people to share her powers with. She has forged a mathematical maze. Only true mathemagicians can solve the puzzles and find their way out. Join two young explorers, Oliviaand Hassan, to solve the puzzles, escape the maze and become the greatest mathemagicians of all time.
Multiplying and dividing by 10, 100 and 1000.
OLIVIA:Wow, that's huge!
HASSAN:Oh it's not that big. Wow, that's huge.
HYPATIA:Ha ha, you've made it to the top. It's a long climb back down again. So if you want to make it through the portal instead, answer me this… There are 139 floors and 10 windows per floor. So, how many windows are there?
OLIVIA:It'll take forever to count them all.
HASSAN:10 windows per floor. There must be an easier way.
HYPATIA:There may well be, perhaps if you ask Archimedes, he could he- Where's Archimedes?
ARCHIMEDES:You can- You can multi- You can multiply. Oh dear.
HYPATIA:Take your time.
OLIVIA:Didn't you take the lift?
ARCHIMEDES:There's a lift? How did you get here before me?
HYPATIA:I can teleport.
ARCHIMEDES:You can teleport?!
HYPATIA:Uh-huh. Good luck with answering my puzzle.
ARCHIMEDES:Oh yes, what we need is a multiplication.
Take 36. We could multiply by 10 by doing a series of additions, adding 36 nine more times, going up the multiples to make 360.
HYPATIA:But notice 360 looks like 36 because it is 36, but 10 times larger. 36 has moved along one place and a placeholder zero has appeared in the ones column.
ARCHIMEDES:So rather than working out the sum, when multiplying by 10 we can simply move the digits to the left, for placeholder zero in the ones column.
HYPATIA:This trick is especially useful when dealing with even larger multiples of 10, even if you don't know your 99 times tables.
ARCHIMEDES:Which most people don't.
HYPATIA:We know our 100 times tables as we simply move our original number along two columns and two placeholders appear in the tens and ones column. So 36 multiplied by 100 is 3600. We could keep going with this. How about multiplying by 1000?
HASSAN:We move 36 three places along because there are three zeros in 1000. Three placeholders appear, so 36 multiplied by 1000 is 36,000.
ARCHIMEDES:Now, if we want to divide by 10, instead of moving our number to the left we simply move it to the right. 36 becomes three point six, note the decimal point we add here. Well, it's really there all the time, but only reveals itself when a part of a number is smaller than one. We put it there to mark the place where our number becomes smaller than a whole number. To divide by 100, we move two, zero point three six. And to divide by 1000, we move three, zero point zero three six.
HYPATIA:So what is 139 times 10 equal to?
HASSAN:So, since there are 139 floors, we can just…
OLIVIA:Take 139…
HASSAN:And multiply by 10.
OLIVIA:It moves to the left one place and a placeholder appears to make…
HASSAN:1390. You can come with us Archimedes.
ARCHIMEDES:Oh that'd be great 'cause I mean, it takes a little while for me to catch up, you know, climbing up here. My calves are exhausted. Oh, back I go…
HYPATIA:Now here is a question for my young mathemagicians. I take the number 247 and divide and multiply it by 10, 100 and 1000. Have a look at my answers. Have I made any mistakes?
Video summary
When Olivia and Hassan find themselves on the roof of an enormous skyscraper they learn how to multiply by 10, 100 and 1000 and work out the number of windows on the building.
Archimedes explains how to multiply by 10, 100 and 1000 - explaining how this method will help Olivia and Hassan work out the number of windows on the skyscraper.
Hypatia concludes the episode with a multiplication question and challenges pupils to find her mistakes in the classroom.
This short animated film is from the BBC Teach series, Hypatia's Mathematical Maze.
Teacher Notes
Before watching the film:
Prior to this lesson you may wish to introduce students to other relevant topics, for example:
- Place value appropriate to the year group
- Multiplication as repeated addition
- The ten times table and its features
During watching the film:
Depending on the focus of your lesson, you may wish to pause the video at certain moments to check for understanding, asking questions such as:
- How many places does the number move when multiplying by 10, 100, 1000 and 10,000?
- How many places does the number move when dividing by 10, 100, 1000 and 10,000?
- How can we tell if a number is a multiple of 10?
- Can you answer Hypatia’s final question?
Final question:Have I made any mistakes?
| x1000 | x100 | x10 | Original number | ÷10 | ÷100 | ÷1000 |
|---|---|---|---|---|---|---|
| 247000 | 24070 | 2470 | 247 | 24.7 | 2.74 | 0.247 |
Answer to the final question:
| x1000 | x100 | x10 | Original number | ÷10 | ÷100 | ÷1000 |
|---|---|---|---|---|---|---|
| 247000 | 24070 | 2470 | 247 | 24.7 | 2.74 | 0.247 |
- x 100 - Place holders have appeared, but not in the correct places. All the digits need to move together, like the figures on a fussball table!
- ÷ 100 - The digits have been switched. Again, all the digits move in the order they were originally.
Following on from the film:
- Use place value sliders to explore how the digits move when multiplying and dividing by 10, 100 and 1000.
- Use ‘backwards’ questions to explore pupils’ efficiency at manipulating the numbers, e.g. I am thinking of a number. I multiply it by 100. My answer is 3650. What was my number?
- Use digit card questions to limit possibilities, e.g. I have the digit cards 1, 2, 3, 4, 5 and 6. Use the cards to fill in the gaps. You may use each digit card once only.
- \(1 - x 100 = - ,300\)
- \(5, - 00 ÷ 100 = - 2\)
- \( - .4 ÷ 10 = 0.6 - \)
This short film is suitable for teaching maths at KS2 in England, Wales and Northern Ireland and 2nd Level in Scotland.
Adding and subtracting using mental methods. video
In a mythical temple full of obstacles, Olivia and Hassan learn simple mental maths and apply it to work out the passcode to open the door.
Adding and subtracting using written methods. video
Having been transported to a floating library, Olivia and Hassan's ability to solve large equations using written methods is tested.
How and why we round numbers. video
Olivia and Hassan are taught how to round to the nearest 1000, 10,000, and 100,000 when a disgruntled magic carpet demands money from them.
Using addition and subtraction in multi-step problems. video
Inside a giant computer created before the age of mathemagicians, Olivia and Hassan are faced with a multi-step problem to reach the labyrinth’s next stage.
Mental multiplication. video
While exploring a jungle, Olivia and Hassan learn the true nature of square numbers as being created when two of the same number are multiplied together.
Factors, multiples and primes. video
Trapped in a desert together with Archimedes, Olivia and Hassan learn what common factors, multiples, and prime numbers are.
Multiplying using written methods. video
Finding themselves in space, Olivia and Hassan watch mathemagician Hypatia perform long multiplications in the sky by bending the stars.
Dividing using written methods. video
Olivia and Hassan learn how to perform long division in order to free gridlocked traffic on a bridge.
Recognising and comparing fractions. video
Olivia and Hassan are enjoying themselves in a world made out of pizza and learn how to work with numerators and denominators in fractions.
Adding and subtracting fractions. video
Amongst the ruins of an ancient city, Olivia and Hassan learn how to add and subtract fractions.
Multiplying and dividing fractions. video
In a mysterious crystal cave, Olivia and Hassan get to work dividing and multiplying fractions in order to find their way out.
